I personally don't as I don't feel I have the knowledge or training to do so, but I go to school with a woman who is a trained vet tech. and she vaccinates her critters at home (except rabies which is done at the vet's)
I know of some breeders who do, but I feel strongly compelled to caution you against it. I don't know how it is where you are, but where I am, vets aren't likely to accept owner/breeder vaccinations. Unless there is a printed statement from another vet's office, most vets around here want to re-vaccinate and will refuse to board/treat an animal unless these statements can be produced. I had a cat scheduled for a dental not too long ago and was told that she would not have the procedure without first receiving her FRCVP booster, which they knew I had administered myself two months prior to this appointment. When I refused to allow them to vaccinate her again since it would mean, IMO, unnecessarily over-vaccinating her, I was told to take my cat home and not to reschedule unless I was willing to allow them to vaccinate her.
Check with your chosen vet to see whether or not they recognize and will accept owner vaccinations before embarking on this path.
I know that my vet back home (who is on the state board of veterinary medicine in Texas) revaccinates kittens who were vaccinated by the breeder because giving vaccines can be moderately tricky. If you leave them out or anything for too long they're no good anymore, and apparently he's had some bad experiences with it.
That being said...my mom has given me a flu vaccination at home before, but she's a registered nurse, so I guess that's okay.
It can be done, but I wouldn't, for the reasons stated above, plus the potential for vaccine reaction. If anything happens, I want a vet to be there to help. (That's also why I schedule the cats' vaccinations at a time when I can be home to observe them afterward, and take them back to the vet if they have any problems.)
One of my cats has had a life-threatening vaccine reaction (anaphylaxis) before, so he needs to be medicated prior to vaccination and observed carefully afterward. A reaction can occur in a cat with no prior adverse vaccine response, so it's always better to be cautious - my cat had his reaction when he was 8 or 9 years old, and had been vaccinated without any problems every year before that.
Also, ther is a protocol for giving cats certain vaccines in certain locations in their body, so that in the rare event a vaccine sarcoma occurs, it can be removed (sarcomas in the back of the neck are difficult or impossible to remove completely), and it can be known which vaccine caused it.
There are many states in the US (mine included) where the rabies vaccine can only be given by a licensed veterinarian. Most vaccine catalogs will list the states where they can't sell rabies vaccine to the general public.
I vaccinate all our adults bengals and kittens myself. It's not something I would recommend for someone who owns one or two cats, but it is best for us in our cattery situation.
All rabies vaccines are given by our vet.
I vaccinate all of my cats and all of my foster cats and kittens myself. I always do it on a day I am going to be home all day to keep an eye on them and first thing in the morning so if they have a reaction and benadryl isn't working I can get them to the vet without having to go to the emergency clinic. As long as I have the stickers from the vaccine bottles on our medical records vets as well as kennels and training centers all accept them. Since I'm the one that receives them I can make sure they are stored properly, etc. I've done probably about 60 of them and so far only one reaction that I got under control without a vet but I certainly hate doing it and rather not have to stick these poor babies!